Finally upgraded to a new Laptop with Windows 8.1. Can I install and run my old Photoshop Elements 5.0 and Premiere Elements 3.0 in the Windows 8.1 environment? I assume the Touchscreen would not work, but otherwise, will it run?

Probably yes to installing Photoshop Elements 5 and Premiere Elements 3 on Windows 8.1 64 bit. You are likely to run into some discouraging "compatibility issues" warnings along the way, but move forward nonetheless. The 5.0.2 Update for Photoshop Elements 5 and the 3.0.2 Update for Premiere Elements 3 are musts once you do manage to get the programs installed.

Also to enhance the probability of success in this task, right click the desktop icon for each and select Run As Administrator.

I have never purchased either of these programs and tried to install them on Windows 8.1 64 bit. But, I have done so successfully with Photoshop Elements 3 on Windows 8.1 64 bit using the maneuvers cited above. I can install Premiere Elements 4 on Windows 8.1 64 bit without problems.